Problem: Simplify the following expression: $r = \dfrac{5y^2 - 95y + 450}{y - 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ r =\dfrac{5(y^2 - 19y + 90)}{y - 9} $ Then we factor the remaining polynomial: $y^2 {-19}y + {90} $ ${-9} {-10} = {-19}$ ${-9} \times {-10} = {90}$ $ (y {-9}) (y {-10}) $ This gives us a factored expression: $\dfrac{5(y {-9}) (y {-10})}{y - 9}$ We can divide the numerator and denominator by $(y + 9)$ on condition that $y \neq 9$ Therefore $r = 5(y - 10); y \neq 9$